According to the majority of scholars, you need to make up for the missed prayers. All you have to do when you are making up for Zuhr Prayer for example is to have in your heart the intention that you are making up for the missed Zuhr Prayer. Do not bother yourself with any more detailed matters that may cause you to fall in doubt and make you confused.
Here we may quote, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, who stated:
Making one’s intention is one of the essential components of prayer, without which it is not valid. The Prophet (peace and blessings be upon him) said: “All actions are rewarded according to intentions.” In other words, where there is no intention to serve Allah, one’s worship is not valid.
the question arises: what is one’s intention in salah? It is to cherish the intention that one is performing such-and-such a prayer to serve Allah. It is not necessary to state the intention verbally as some people believe. Such a practice was never prevalent during the time of the Prophet (peace and blessings be upon him) or the early Muslims, whose example we must strive to follow.